The generalized recurrent set, explosions and Lyapunov functions

Abstract : We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contrast to the case for the chain recurrent set. We give sufficient conditions to avoid explosions and discuss their necessity. Moreover, we explain the relations between explosions and cycles for the generalized recurrent set. In particular, for a compact topological manifold with dimension greater or equal 2, we characterize explosion phenomena in terms of existence of cycles. We apply our results to give sufficient conditions for stability, under C 0 perturbations, of the property of admitting a continuous Lyapunov function which is not a first integral.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal-univ-avignon.archives-ouvertes.fr/hal-02097706
Contributor : Anna Florio <>
Submitted on : Friday, April 12, 2019 - 10:55:35 AM
Last modification on : Tuesday, April 16, 2019 - 1:27:51 AM

File

GR-explosions-Lyapunov-OB-AF-J...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02097706, version 1

Collections

Citation

Olga Bernardi, Anna Florio, Jim Wiseman. The generalized recurrent set, explosions and Lyapunov functions. 2019. ⟨hal-02097706⟩

Share

Metrics

Record views

32

Files downloads

75